List edge and list total colourings of multigraphs
Journal of Combinatorial Theory Series B
List edge and list total colorings of planar graphs without 4-cycles
Theoretical Computer Science
On the linear arboricity of planar graphs
Journal of Graph Theory
List edge and list total colorings of planar graphs without short cycles
Information Processing Letters
Graph Theory
On the total choosability of planar graphs and of sparse graphs
Information Processing Letters
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In this note, we prove a structural theorem for planar graphs, namely that every planar graph has one of four possible configurations: (1) a vertex of degree 1, (2) intersecting triangles, (3) an edge xy with d(x)+d(y)@?9, (4) a 2-alternating cycle. Applying this theorem, new moderate results on edge choosability, total choosability, edge-partitions and linear arboricity of planar graphs are obtained.